Quasicrystals are substances whose molecular structure is ordered in a form similar to crystals but is not periodic. Such materials can naturally form into geometrical solids just as crystals can, but the solids formed from crystals are always shapes that can tessellate space, such as a cube. Quasicrystals on the other hand can form shapes such as a dodecahedron. The mathematical patterns that describe the layouts of the molecules were studied by Roger Penrose but have also been found in some ancient arabic art.
Shechtman was the first to make such crystals in 1984.